Introducción a la Economía

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# Introducción a la<br>Economía 
## **Crecimiento económico**
### Carlos A. Yanes Guerra
### 9 de Noviembre, 2023

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# 😓

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# Preguntas de las sesiones anteriores?
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# Crecimiento Económico 📈

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# Un par de preguntas

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# Ideas generales 🔉
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# Ideas generales

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![](data:image/png;base64,#Clase12_files/figure-html/graph01-1.svg)

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## Calculos

La tasa de .hi[crecimiento] normalmente viene a ser:

<font size="+5">$$Crecimiento=\left[\frac{Y_{t}}{Y_{t-1}}-1\right]\times 100$$</font>

Donde `$Y_{t}$` hace referencia al PIB per capita en el .hi-turquoise[periodo presente] y `$Y_{t-1}$` al PIB per cápita del periodo anterior.

>En algunas ocasiones puede haber un **crecimiento exponencial**, esto es, el PIB per cápita crece a una tasa constante

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*Cada año se gana un 8%* de tal manera que el crecimiento total entonces es de `$0.08 \times 15= 1.2$`
--
 es lo mismo que
--
`$Y_{2025}=Y_{2020}\times (1.2)\dots$` .hi-purple[falso!!!]

En realidad es una sucesión... mire a continuación

- `$Y_{2021}=Y_{2020}\times (1.08)$`

- `$Y_{2022}=Y_{2021}\times (1.08)=Y_{2020}\times (1.08)\times (1.08)= Y_{2020}\times (1.08)^2$`

- `$Y_{2023}=Y_{2022}\times (1.08)=Y_{2020}\times (1.08)^2\times (1.08)= Y_{2020}\times (1.08)^3$`

- `$Y_{2024}=Y_{2023}\times (1.08)=Y_{2020}\times (1.08)^3\times (1.08)= Y_{2020}\times (1.08)^4$`

`$\cdots$` y así hasta llegar a 2025

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- `$Y_{2025}=\color{red}{Y_{2020}\times (1.08)^5}=\color{purple}{Y_{2020}\times 1.46} > Y_{2020} \times 0.50$`

- `$Y_{2030}=\color{red}{Y_{2020}\times (1.08)^{10}}=\color{blue}{Y_{2020}\times 2.15} > Y_{2020} \times 1.00$`

- `$Y_{2035}=\color{red}{Y_{2020}\times (1.08)^{15}}=\color{darkblue}{Y_{2020}\times 3.17} > Y_{2020} \times 1.50$`

De esto surge que para comparar distintos .hi[países] toca resaltar la .ul[escala proporcional].

- Un .hi-purple[crecimiento] del 8% por ejemplo, nos llevará un capital de 1000 a 1080 con un cambio de 80.

- Un .hi-purple[crecimiento] del 8% por ejemplo, nos llevará un capital de 10000 a 10800 con un cambio de 800.

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![](data:image/png;base64,#Clase12_files/figure-html/graph02-1.svg)

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# Miremos la escala proporcional

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# Poder del Crecimiento
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![](data:image/png;base64,#Clase12_files/figure-html/graph03-1.svg)

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.hi[Cúal seria el PIB en 2020 (200 años) si cada uno de ellos crece a tasas del 0%, 1% y 2% respectivamente?]

R./

- `$Y_{2020}= 1000$`

- `$Y_{2020}= 7316$`

- `$Y_{2020}= 52485$`

`$$PIB \times (1+\text{Tasa de Crec.})^{\text{Tiempo}}$$`
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<table class="table table-striped table-hover table-condensed table-responsive" style="margin-left: auto; margin-right: auto;">
<caption>Tabla de PIB y Crecimiento</caption>
 <thead>
  <tr>
   <th style="text-align:center;"> País </th>
   <th style="text-align:center;"> PIB.1960 </th>
   <th style="text-align:center;"> PIB.2020 </th>
   <th style="text-align:center;"> Crecimiento </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> Luxemburgo </td>
   <td style="text-align:center;background-color: #FFA500 !important;"> 17601 </td>
   <td style="text-align:center;background-color: #FFA500 !important;"> 75589 </td>
   <td style="text-align:center;background-color: #FFA500 !important;"> 2.9% </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Singapur </td>
   <td style="text-align:center;background-color: #f92672 !important;"> 4383 </td>
   <td style="text-align:center;background-color: #f92672 !important;"> 55862 </td>
   <td style="text-align:center;background-color: #f92672 !important;"> 5.22% </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Nigeria </td>
   <td style="text-align:center;background-color: #44C1C4 !important;"> 861 </td>
   <td style="text-align:center;background-color: #44C1C4 !important;"> 522 </td>
   <td style="text-align:center;background-color: #44C1C4 !important;"> -1.00% </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Estados Unidos </td>
   <td style="text-align:center;background-color: #FFA500 !important;"> 15398 </td>
   <td style="text-align:center;background-color: #FFA500 !important;"> 41365 </td>
   <td style="text-align:center;background-color: #FFA500 !important;"> 2.00% </td>
  </tr>
  <tr>
   <td style="text-align:center;"> Corea del Sur </td>
   <td style="text-align:center;background-color: #f92672 !important;"> 1656 </td>
   <td style="text-align:center;background-color: #f92672 !important;"> 26609 </td>
   <td style="text-align:center;background-color: #f92672 !important;"> 5.71% </td>
  </tr>
</tbody>
</table>

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# Por qué crece un país 📈
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# Por qué crecemos

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Hay que tener muy presente la función de producción *teórica*:

<font size="+5">$$Y=A \times F(K, L)$$</font>

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![](data:image/png;base64,#https://media.giphy.com/media/NyniJ2Nf2ZzlE8GYsl/giphy.gif)
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> Qué determina el ahorro?

R./ .hi[Los hogares]
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<font size="+5">$$\text{Tasa de Ahorro}=\frac{\text{Ahorro Total}}{PIB}$$</font>

La acumulación de capital físico por si sola no puede generar **crecimiento sostenido** ya que siempre la productividad marginal es decreciente.

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![](data:image/png;base64,#Clase12_files/figure-html/graph04-1.svg)

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.hi-purple[P:] ¿ Por qué somos más prosperos que nuestros tatarabuelos?

.hi[R./] En la gran mayoría de décadas, .hi-turquoise[tecnología] es la que mas contribuye al PIB por trabajador por lo menos en un páis como los EEUU.

<center>
<span style="color:blue"> 
No podemos igual infravalorar el trabajo humano, porque de ser así podríamos exagerar la contribución de la tecnología
</span>
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La .hi-turquoise[tecnología] no tiene rendimientos decrecientes, regularmente lo que ya sabemos es porque antes se desarrolló con alta intensidad.

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# Historia del crecimiento 🔧

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# Historia del crecimiento

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La .hi[historia] económica del mundo puede dividirse en tres periodos:
1. .hi-orange[Pre-modernidad] hasta 1800
2. .hi-pink[Revolución industrial] De 1800 a 1820
3. .hi-orange[Post-revolución industrial] hasta 1820 hasta hoy
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<img src="data:image/png;base64,#https://media.giphy.com/media/xT5LMXA2FClO5yvy80/giphy.gif" class="scaled-image" />
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.pull-right[
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<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M220.8 123.3c1 .5 1.8 1.7 3 1.7 1.1 0 2.8-.4 2.9-1.5.2-1.4-1.9-2.3-3.2-2.9-1.7-.7-3.9-1-5.5-.1-.4.2-.8.7-.6 1.1.3 1.3 2.3 1.1 3.4 1.7zm-21.9 1.7c1.2 0 2-1.2 3-1.7 1.1-.6 3.1-.4 3.5-1.6.2-.4-.2-.9-.6-1.1-1.6-.9-3.8-.6-5.5.1-1.3.6-3.4 1.5-3.2 2.9.1 1 1.8 1.5 2.8 1.4zM420 403.8c-3.6-4-5.3-11.6-7.2-19.7-1.8-8.1-3.9-16.8-10.5-22.4-1.3-1.1-2.6-2.1-4-2.9-1.3-.8-2.7-1.5-4.1-2 9.2-27.3 5.6-54.5-3.7-79.1-11.4-30.1-31.3-56.4-46.5-74.4-17.1-21.5-33.7-41.9-33.4-72C311.1 85.4 315.7.1 234.8 0 132.4-.2 158 103.4 156.9 135.2c-1.7 23.4-6.4 41.8-22.5 64.7-18.9 22.5-45.5 58.8-58.1 96.7-6 17.9-8.8 36.1-6.2 53.3-6.5 5.8-11.4 14.7-16.6 20.2-4.2 4.3-10.3 5.9-17 8.3s-14 6-18.5 14.5c-2.1 3.9-2.8 8.1-2.8 12.4 0 3.9.6 7.9 1.2 11.8 1.2 8.1 2.5 15.7.8 20.8-5.2 14.4-5.9 24.4-2.2 31.7 3.8 7.3 11.4 10.5 20.1 12.3 17.3 3.6 40.8 2.7 59.3 12.5 19.8 10.4 39.9 14.1 55.9 10.4 11.6-2.6 21.1-9.6 25.9-20.2 12.5-.1 26.3-5.4 48.3-6.6 14.9-1.2 33.6 5.3 55.1 4.1.6 2.3 1.4 4.6 2.5 6.7v.1c8.3 16.7 23.8 24.3 40.3 23 16.6-1.3 34.1-11 48.3-27.9 13.6-16.4 36-23.2 50.9-32.2 7.4-4.5 13.4-10.1 13.9-18.3.4-8.2-4.4-17.3-15.5-29.7zM223.7 87.3c9.8-22.2 34.2-21.8 44-.4 6.5 14.2 3.6 30.9-4.3 40.4-1.6-.8-5.9-2.6-12.6-4.9 1.1-1.2 3.1-2.7 3.9-4.6 4.8-11.8-.2-27-9.1-27.3-7.3-.5-13.9 10.8-11.8 23-4.1-2-9.4-3.5-13-4.4-1-6.9-.3-14.6 2.9-21.8zM183 75.8c10.1 0 20.8 14.2 19.1 33.5-3.5 1-7.1 2.5-10.2 4.6 1.2-8.9-3.3-20.1-9.6-19.6-8.4.7-9.8 21.2-1.8 28.1 1 .8 1.9-.2-5.9 5.5-15.6-14.6-10.5-52.1 8.4-52.1zm-13.6 60.7c6.2-4.6 13.6-10 14.1-10.5 4.7-4.4 13.5-14.2 27.9-14.2 7.1 0 15.6 2.3 25.9 8.9 6.3 4.1 11.3 4.4 22.6 9.3 8.4 3.5 13.7 9.7 10.5 18.2-2.6 7.1-11 14.4-22.7 18.1-11.1 3.6-19.8 16-38.2 14.9-3.9-.2-7-1-9.6-2.1-8-3.5-12.2-10.4-20-15-8.6-4.8-13.2-10.4-14.7-15.3-1.4-4.9 0-9 4.2-12.3zm3.3 334c-2.7 35.1-43.9 34.4-75.3 18-29.9-15.8-68.6-6.5-76.5-21.9-2.4-4.7-2.4-12.7 2.6-26.4v-.2c2.4-7.6.6-16-.6-23.9-1.2-7.8-1.8-15 .9-20 3.5-6.7 8.5-9.1 14.8-11.3 10.3-3.7 11.8-3.4 19.6-9.9 5.5-5.7 9.5-12.9 14.3-18 5.1-5.5 10-8.1 17.7-6.9 8.1 1.2 15.1 6.8 21.9 16l19.6 35.6c9.5 19.9 43.1 48.4 41 68.9zm-1.4-25.9c-4.1-6.6-9.6-13.6-14.4-19.6 7.1 0 14.2-2.2 16.7-8.9 2.3-6.2 0-14.9-7.4-24.9-13.5-18.2-38.3-32.5-38.3-32.5-13.5-8.4-21.1-18.7-24.6-29.9s-3-23.3-.3-35.2c5.2-22.9 18.6-45.2 27.2-59.2 2.3-1.7.8 3.2-8.7 20.8-8.5 16.1-24.4 53.3-2.6 82.4.6-20.7 5.5-41.8 13.8-61.5 12-27.4 37.3-74.9 39.3-112.7 1.1.8 4.6 3.2 6.2 4.1 4.6 2.7 8.1 6.7 12.6 10.3 12.4 10 28.5 9.2 42.4 1.2 6.2-3.5 11.2-7.5 15.9-9 9.9-3.1 17.8-8.6 22.3-15 7.7 30.4 25.7 74.3 37.2 95.7 6.1 11.4 18.3 35.5 23.6 64.6 3.3-.1 7 .4 10.9 1.4 13.8-35.7-11.7-74.2-23.3-84.9-4.7-4.6-4.9-6.6-2.6-6.5 12.6 11.2 29.2 33.7 35.2 59 2.8 11.6 3.3 23.7.4 35.7 16.4 6.8 35.9 17.9 30.7 34.8-2.2-.1-3.2 0-4.2 0 3.2-10.1-3.9-17.6-22.8-26.1-19.6-8.6-36-8.6-38.3 12.5-12.1 4.2-18.3 14.7-21.4 27.3-2.8 11.2-3.6 24.7-4.4 39.9-.5 7.7-3.6 18-6.8 29-32.1 22.9-76.7 32.9-114.3 7.2zm257.4-11.5c-.9 16.8-41.2 19.9-63.2 46.5-13.2 15.7-29.4 24.4-43.6 25.5s-26.5-4.8-33.7-19.3c-4.7-11.1-2.4-23.1 1.1-36.3 3.7-14.2 9.2-28.8 9.9-40.6.8-15.2 1.7-28.5 4.2-38.7 2.6-10.3 6.6-17.2 13.7-21.1.3-.2.7-.3 1-.5.8 13.2 7.3 26.6 18.8 29.5 12.6 3.3 30.7-7.5 38.4-16.3 9-.3 15.7-.9 22.6 5.1 9.9 8.5 7.1 30.3 17.1 41.6 10.6 11.6 14 19.5 13.7 24.6zM173.3 148.7c2 1.9 4.7 4.5 8 7.1 6.6 5.2 15.8 10.6 27.3 10.6 11.6 0 22.5-5.9 31.8-10.8 4.9-2.6 10.9-7 14.8-10.4s5.9-6.3 3.1-6.6-2.6 2.6-6 5.1c-4.4 3.2-9.7 7.4-13.9 9.8-7.4 4.2-19.5 10.2-29.9 10.2s-18.7-4.8-24.9-9.7c-3.1-2.5-5.7-5-7.7-6.9-1.5-1.4-1.9-4.6-4.3-4.9-1.4-.1-1.8 3.7 1.7 6.5z"/></svg> Si ayuda a contener y es un .turquoise[instrumento] para ello
<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M220.8 123.3c1 .5 1.8 1.7 3 1.7 1.1 0 2.8-.4 2.9-1.5.2-1.4-1.9-2.3-3.2-2.9-1.7-.7-3.9-1-5.5-.1-.4.2-.8.7-.6 1.1.3 1.3 2.3 1.1 3.4 1.7zm-21.9 1.7c1.2 0 2-1.2 3-1.7 1.1-.6 3.1-.4 3.5-1.6.2-.4-.2-.9-.6-1.1-1.6-.9-3.8-.6-5.5.1-1.3.6-3.4 1.5-3.2 2.9.1 1 1.8 1.5 2.8 1.4zM420 403.8c-3.6-4-5.3-11.6-7.2-19.7-1.8-8.1-3.9-16.8-10.5-22.4-1.3-1.1-2.6-2.1-4-2.9-1.3-.8-2.7-1.5-4.1-2 9.2-27.3 5.6-54.5-3.7-79.1-11.4-30.1-31.3-56.4-46.5-74.4-17.1-21.5-33.7-41.9-33.4-72C311.1 85.4 315.7.1 234.8 0 132.4-.2 158 103.4 156.9 135.2c-1.7 23.4-6.4 41.8-22.5 64.7-18.9 22.5-45.5 58.8-58.1 96.7-6 17.9-8.8 36.1-6.2 53.3-6.5 5.8-11.4 14.7-16.6 20.2-4.2 4.3-10.3 5.9-17 8.3s-14 6-18.5 14.5c-2.1 3.9-2.8 8.1-2.8 12.4 0 3.9.6 7.9 1.2 11.8 1.2 8.1 2.5 15.7.8 20.8-5.2 14.4-5.9 24.4-2.2 31.7 3.8 7.3 11.4 10.5 20.1 12.3 17.3 3.6 40.8 2.7 59.3 12.5 19.8 10.4 39.9 14.1 55.9 10.4 11.6-2.6 21.1-9.6 25.9-20.2 12.5-.1 26.3-5.4 48.3-6.6 14.9-1.2 33.6 5.3 55.1 4.1.6 2.3 1.4 4.6 2.5 6.7v.1c8.3 16.7 23.8 24.3 40.3 23 16.6-1.3 34.1-11 48.3-27.9 13.6-16.4 36-23.2 50.9-32.2 7.4-4.5 13.4-10.1 13.9-18.3.4-8.2-4.4-17.3-15.5-29.7zM223.7 87.3c9.8-22.2 34.2-21.8 44-.4 6.5 14.2 3.6 30.9-4.3 40.4-1.6-.8-5.9-2.6-12.6-4.9 1.1-1.2 3.1-2.7 3.9-4.6 4.8-11.8-.2-27-9.1-27.3-7.3-.5-13.9 10.8-11.8 23-4.1-2-9.4-3.5-13-4.4-1-6.9-.3-14.6 2.9-21.8zM183 75.8c10.1 0 20.8 14.2 19.1 33.5-3.5 1-7.1 2.5-10.2 4.6 1.2-8.9-3.3-20.1-9.6-19.6-8.4.7-9.8 21.2-1.8 28.1 1 .8 1.9-.2-5.9 5.5-15.6-14.6-10.5-52.1 8.4-52.1zm-13.6 60.7c6.2-4.6 13.6-10 14.1-10.5 4.7-4.4 13.5-14.2 27.9-14.2 7.1 0 15.6 2.3 25.9 8.9 6.3 4.1 11.3 4.4 22.6 9.3 8.4 3.5 13.7 9.7 10.5 18.2-2.6 7.1-11 14.4-22.7 18.1-11.1 3.6-19.8 16-38.2 14.9-3.9-.2-7-1-9.6-2.1-8-3.5-12.2-10.4-20-15-8.6-4.8-13.2-10.4-14.7-15.3-1.4-4.9 0-9 4.2-12.3zm3.3 334c-2.7 35.1-43.9 34.4-75.3 18-29.9-15.8-68.6-6.5-76.5-21.9-2.4-4.7-2.4-12.7 2.6-26.4v-.2c2.4-7.6.6-16-.6-23.9-1.2-7.8-1.8-15 .9-20 3.5-6.7 8.5-9.1 14.8-11.3 10.3-3.7 11.8-3.4 19.6-9.9 5.5-5.7 9.5-12.9 14.3-18 5.1-5.5 10-8.1 17.7-6.9 8.1 1.2 15.1 6.8 21.9 16l19.6 35.6c9.5 19.9 43.1 48.4 41 68.9zm-1.4-25.9c-4.1-6.6-9.6-13.6-14.4-19.6 7.1 0 14.2-2.2 16.7-8.9 2.3-6.2 0-14.9-7.4-24.9-13.5-18.2-38.3-32.5-38.3-32.5-13.5-8.4-21.1-18.7-24.6-29.9s-3-23.3-.3-35.2c5.2-22.9 18.6-45.2 27.2-59.2 2.3-1.7.8 3.2-8.7 20.8-8.5 16.1-24.4 53.3-2.6 82.4.6-20.7 5.5-41.8 13.8-61.5 12-27.4 37.3-74.9 39.3-112.7 1.1.8 4.6 3.2 6.2 4.1 4.6 2.7 8.1 6.7 12.6 10.3 12.4 10 28.5 9.2 42.4 1.2 6.2-3.5 11.2-7.5 15.9-9 9.9-3.1 17.8-8.6 22.3-15 7.7 30.4 25.7 74.3 37.2 95.7 6.1 11.4 18.3 35.5 23.6 64.6 3.3-.1 7 .4 10.9 1.4 13.8-35.7-11.7-74.2-23.3-84.9-4.7-4.6-4.9-6.6-2.6-6.5 12.6 11.2 29.2 33.7 35.2 59 2.8 11.6 3.3 23.7.4 35.7 16.4 6.8 35.9 17.9 30.7 34.8-2.2-.1-3.2 0-4.2 0 3.2-10.1-3.9-17.6-22.8-26.1-19.6-8.6-36-8.6-38.3 12.5-12.1 4.2-18.3 14.7-21.4 27.3-2.8 11.2-3.6 24.7-4.4 39.9-.5 7.7-3.6 18-6.8 29-32.1 22.9-76.7 32.9-114.3 7.2zm257.4-11.5c-.9 16.8-41.2 19.9-63.2 46.5-13.2 15.7-29.4 24.4-43.6 25.5s-26.5-4.8-33.7-19.3c-4.7-11.1-2.4-23.1 1.1-36.3 3.7-14.2 9.2-28.8 9.9-40.6.8-15.2 1.7-28.5 4.2-38.7 2.6-10.3 6.6-17.2 13.7-21.1.3-.2.7-.3 1-.5.8 13.2 7.3 26.6 18.8 29.5 12.6 3.3 30.7-7.5 38.4-16.3 9-.3 15.7-.9 22.6 5.1 9.9 8.5 7.1 30.3 17.1 41.6 10.6 11.6 14 19.5 13.7 24.6zM173.3 148.7c2 1.9 4.7 4.5 8 7.1 6.6 5.2 15.8 10.6 27.3 10.6 11.6 0 22.5-5.9 31.8-10.8 4.9-2.6 10.9-7 14.8-10.4s5.9-6.3 3.1-6.6-2.6 2.6-6 5.1c-4.4 3.2-9.7 7.4-13.9 9.8-7.4 4.2-19.5 10.2-29.9 10.2s-18.7-4.8-24.9-9.7c-3.1-2.5-5.7-5-7.7-6.9-1.5-1.4-1.9-4.6-4.3-4.9-1.4-.1-1.8 3.7 1.7 6.5z"/></svg> La brecha de desigualdad debe reducirse y esto implica mucha intervención y aparte voluntad social
]

---
layout: false
# Bibliografía

---
name: adios
class: middle, inverse

.pull-left[
# **¡Gracias!**
<br/>
## Crecimiento

### Este es el final del curso
]

.pull-right[
.right[
<img style="border-radius: 50%;"
src="https://avatars.githubusercontent.com/u/39503983?v=4"
width="150px" />

[<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M579.8 267.7c56.5-56.5 56.5-148 0-204.5c-50-50-128.8-56.5-186.3-15.4l-1.6 1.1c-14.4 10.3-17.7 30.3-7.4 44.6s30.3 17.7 44.6 7.4l1.6-1.1c32.1-22.9 76-19.3 103.8 8.6c31.5 31.5 31.5 82.5 0 114L422.3 334.8c-31.5 31.5-82.5 31.5-114 0c-27.9-27.9-31.5-71.8-8.6-103.8l1.1-1.6c10.3-14.4 6.9-34.4-7.4-44.6s-34.4-6.9-44.6 7.4l-1.1 1.6C206.5 251.2 213 330 263 380c56.5 56.5 148 56.5 204.5 0L579.8 267.7zM60.2 244.3c-56.5 56.5-56.5 148 0 204.5c50 50 128.8 56.5 186.3 15.4l1.6-1.1c14.4-10.3 17.7-30.3 7.4-44.6s-30.3-17.7-44.6-7.4l-1.6 1.1c-32.1 22.9-76 19.3-103.8-8.6C74 372 74 321 105.5 289.5L217.7 177.2c31.5-31.5 82.5-31.5 114 0c27.9 27.9 31.5 71.8 8.6 103.9l-1.1 1.6c-10.3 14.4-6.9 34.4 7.4 44.6s34.4 6.9 44.6-7.4l1.1-1.6C433.5 260.8 427 182 377 132c-56.5-56.5-148-56.5-204.5 0L60.2 244.3z"/></svg> Syllabus/ Curso](https://pomelo.uninorte.edu.co/pls/prod/bwckctlg.p_disp_course_detail?cat_term_in=202210&subj_code_in=ECO&crse_numb_in=0010)<br/>
[<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg> @keynes37](https://twitter.com/keynes37)<br/>
[<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M16.1 260.2c-22.6 12.9-20.5 47.3 3.6 57.3L160 376V479.3c0 18.1 14.6 32.7 32.7 32.7c9.7 0 18.9-4.3 25.1-11.8l62-74.3 123.9 51.6c18.9 7.9 40.8-4.5 43.9-24.7l64-416c1.9-12.1-3.4-24.3-13.5-31.2s-23.3-7.5-34-1.4l-448 256zm52.1 25.5L409.7 90.6 190.1 336l1.2 1L68.2 285.7zM403.3 425.4L236.7 355.9 450.8 116.6 403.3 425.4z"/></svg> cayanes@uninorte.edu.co](mailto:cayanes@uninorte.edu.co)
]
]

???
¡Gracias por tu atención! 
En este momento me encantaría tomar preguntas y si me quieren contactar no olviden enviar un email.